Add files via upload

CEopt-1.0/CEopt.m

@@ -1,11 +1,11 @@
 % -----------------------------------------------------------------
 %  CEopt.m
 % -----------------------------------------------------------------
-%  programmer: Americo Cunha Jr
+%  Programmer: Americo Cunha Jr
 %              [email protected]
 %
 %  Originally programmed in: Jun 18, 2021
-%           Last updated in: Apr 10, 2024
+%           Last updated in: Aug 15, 2024
 % -----------------------------------------------------------------
 %  This routine employs the Cross-entropy (CE) method to solve the 
 %  following optimization problem:
@@ -106,12 +106,32 @@
 %  CEstr   -  The updated Cross-Entropy object struct containing the final
 %             state  of  the  algorithm and possibly additional diagnostic
 %             information.
+% -----------------------------------------------------------------
+%  References:
 %  
-%  Reference:
-%  Reuven Y. Rubinstein, Dirk P. Kroese
-%  The Cross-Entropy Method: A Unified Approach to Combinatorial 
-%  Optimization, Monte-Carlo Simulation, and Machine Learning
-%  Springer-Verlag, 2004.
+%  [1] Reuven Y. Rubinstein, Dirk P. Kroese,
+%      The Cross-Entropy Method: A Unified Approach to Combinatorial 
+%      Optimization, Monte-Carlo Simulation, and Machine Learning,
+%      Springer-Verlag, 2004.
+%  
+%  [2] A. Cunha Jr, M. V. Issa, J. C. Basilio, J. G. Telles Ribeiro,
+%      CEopt: A MATLAB Package for Non-convex Optimization with the
+%      Cross-Entropy Method, ArXiv, 2024
+% -----------------------------------------------------------------
+%  Copyright (C) 2024  Americo Cunha Jr et al.
+% 
+%  This program is free software: you can redistribute it and/or modify
+%  it under the terms of the GNU General Public License as published by
+%  the Free Software Foundation, either version 3 of the License, or
+%  (at your option) any later version.
+%
+%  This program is distributed in the hope that it will be useful,
+%  but WITHOUT ANY WARRANTY; without even the implied warranty of
+%  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%  GNU General Public License for more details.
+%
+%  You should have received a copy of the GNU General Public License
+%  along with this program. If not, see <https://www.gnu.org/licenses/>.
 % -----------------------------------------------------------------
 function [Xopt,Fopt,ExitFlag,CEstr] = ...
                     CEopt(fun,xmean0,sigma0,lb,ub,nonlcon,CEstr)

CEopt-1.0/MainCEoptExample1Ext.m

@@ -33,7 +33,7 @@
 
 % CE optimizer
 tic
-[Xopt,Fopt,ExitFlag,CEobj] = CEopt(F,mu0,sigma0,lb,ub)
+[Xopt,Fopt,ExitFlag,CEstr] = CEopt(F,mu0,sigma0,lb,ub)
 toc
 
 % domain for plotting

CEopt-1.0/MainCEoptExample2.m

@@ -28,7 +28,7 @@
 
 % CE optimizer
 tic
-[X_opt,F_opt,ExitFlag,CEstr] = CEopt(F,mu0,sigma0,lb,ub,[],CEstr)
+[Xopt,Fopt,ExitFlag,CEstr] = CEopt(F,mu0,sigma0,lb,ub,[],CEstr)
 toc
 
 % objective function

CEopt-1.0/MainCEoptExample5.m

@@ -30,7 +30,7 @@
     thetaA = p(3,:);
     a0     = 1;
     b0     = x(1);
-    c0     = b0;
+    c0     = x(1);
     d0     = x(2);
     gamma  = x(3);
     thetaD = x(4);
@@ -49,5 +49,7 @@
     xEc1 = (xEc0 - mean(xEc0))/(max(xEc0) - min(xEc0));
     yEc1 = (yEc0 - mean(yEc0))/(max(xEc0) - min(xEc0));
 
-    F = sum(abs(xE1 - xEc1) + abs(yE1 - yEc1));
+    F1 = sum((xE1 - real(xEc1)).^2 + (yE1 - real(yEc1)).^2);
+    F2 = sum(abs(imag(xEc1).^2) + abs(imag(yEc1).^2) + abs(imag(thetaB).^2));
+    F  = F1 + F2;
 end

CEopt-1.0/MainCEoptExample7.m

@@ -0,0 +1,47 @@
+clc; clear; close all;
+
+disp(' ------------------- ')
+disp(' MainCEoptExample6Ext.m ')
+disp(' ------------------- ')
+
+% bound for design variables
+lb = [-6 -4];
+ub = [ 2  4];
+
+% objective function and constraints
+F       = @PatternSearchFunc;
+nonlcon = @ConicConstraints;
+
+% cross-entropy optimizer struct
+CEobj.isVectorized  = 1;       % vectorized function
+CEobj.TolCon        = 1.0e-6;  % relative tolerance
+
+tic
+[Xopt,Fopt,ExitFlag,CEobj] = CEopt(F,[],[],lb,ub,nonlcon,CEobj)
+toc
+
+% objective function
+function F = PatternSearchFunc(x)
+    x1 = x(:,1);
+    x2 = x(:,2);
+    F = zeros(size(x1,1),1);
+    for i = 1:size(x,1)
+        if  x1(i) < -5
+            F(i) = (x1(i)+5).^2 + abs(x2(i));
+        elseif x1(i) < -3
+            F(i) = -2*sin(x1(i)) + abs(x2(i));
+        elseif x1(i) < 0
+            F(i) = 0.5*x1(i) + 2 + abs(x2(i));
+        elseif x1 >= 0
+            F(i) = .3*sqrt(x1(i)) + 5/2 + abs(x2(i));
+        end
+    end
+end
+
+% equality and inequality constraints
+function [G,H] = ConicConstraints(x)
+    x1 = x(:,1);
+    x2 = x(:,2);
+    G  = 2*x1.^2 + x2.^2 - 3;
+    H  = (x1+1).^2 - (x2/2).^4;
+end